This is a practice problem from Ross (A First Course in Probability)

An interviewer is given a list of people she can interview. If the interviewer needs to interview 5 people, and if each person (independently agrees to be interviewed with probability 2/3, what is the probability that her list of people will enable her to obtain her necessary number of interviews if the list consists of (a) 5 people and (b) 8 people? For part (b), what is the probability that the interviewer will speak to exactly (c) 6 people and (d) 7 people?

(a) and (b) were super easy... they were just a negative binomial dist with p= 2/3 and X=5 one for n=5 and one for n=8

now for calculating the exact number, I am a bit confused. any hints?

I'm usually a genius in this class but this problem has me stumped!

I've tried everything